Final answer:
The quadratic expression 5n^2 + 7n + 2 can be factored as (5n + 2)(n + 1) by finding two numbers that multiply to give a product of 10 and add up to 7, which are 5 and 2.
Step-by-step explanation:
To factor the quadratic expression 5n^2 + 7n + 2, you are looking for two binomials that multiply together to give you the original expression. The process is also known as factoring by grouping. To factor this, you look for two numbers that multiply to give you the product of the coefficient of n^2 (which is 5) and the constant term (which is 2), which is 10, and that add up to give you the coefficient of n (which is 7).
The two numbers that satisfy these conditions are 5 and 2 because 5 * 2 = 10 and 5 + 2 = 7. This means the expression can be factored as (5n + 2)(n + 1), which corresponds to option B).